Finger of Death is a [Death] effect
Note the brackets: what I’m getting at is that you know whether or not something is a Death effect by whether or not it has that [Death] descriptor:
Finger of Death
Not everything that kills is a Death effect. If it’s a spell that doesn’t have the [Death] descriptor, or a non-spell that doesn’t state that it is a Death effect (for example, the Assassin’s Death Attack does not and is not a Death effect [edit: but see @Ernir’s answer for some problems with that]). This is very important for things like raise dead and death ward.
Unfortunately, Wizards wasn’t always super-careful about stating that things that kill are Death effects, which means that some things that probably should be don’t actually have it (but some things that don’t really aren’t supposed to have it). You may have to rule on the fly about such things (such as in the case of Death Attack itself, per @Ernir's answer). Generally speaking, the more descriptors a thing has, the more likely a creature is to have resistance or immunity to it; being able to kill without the Death descriptor is great because then it ignores death ward and the like. Sometimes that advantage is an intended part of a power; other times, it’s not and the lack of descriptor is an oversight. It is hard to say for sure in most cases.
Finger of Death doesn’t have anything to do with the Undead
Just because it’s in the Necromancy school doesn’t mean that it causes undeath or has anything to do with them. Most Sorcerer/Wizard necromancy spells actually don’t; they favor curses and debuffs over animation.
Resurrection doesn’t care about Death effects
Just to note, the resurrection spell (and, by extension, true resurrection) doesn’t care if the target was killed with a Death effect.